Demystifier said:
The so called "Copenhagen" interpretation of QM, known also as "standard" or "orthodox" interpretation, which is really a wide class of related but different interpretations, is often formulated as a statement that some things cannot be known. For instance, one cannot know both position and momentum of the particle at the same time.
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But on other hand, it is also not rare that one formulates such an interpretation as a statement that some things don't exist. For instance, position and momentum of the particle don't exist at the same time.
Which of those two formulations better describes the spirit of Copenhagen/standard/orthodox interpretations?
What you have described here is not Copenhagen. What you have written is very much closer to the notion of
Complementarity (as promoted by Wilczek, et al). A litte more about this below, but to circle back to Copenhagen briefly,
Copenhagen consists of three main pillars.
1. There are things in the world called "observers" (which correspond to our intuitive notion of people/scientists/grad students).
2. There are events in the world called "measurements" (which correspond with our intuitive notion of measuring a system.)
3. It does not make sense to ask about a particle's position prior to measurement. In another thread you quoted Bohr's remark that QM is a theory about what is measured, not what is "out there" in the world.
Copenhagen was satisfactory in the early years of the theory, since no serious scientists was going to demand a formal definition of a human observer, or ask pathological questions about "measurement". Eventually, everyone did both things, giving rise to a pantheon of various modern interpretations. "observers" are also made of particles, and "measurement" is reformulated as some kind of
information copying.
Contemporary notions of Complementarity use the verb "to know" for a specific reason. Any information about the system's state could be stored somewhere independent of the act of measurement (say in the RAM of a computer). It appears, for all intents, that the mere possibility of an observer being able to retreive this information is enough, by itself, to remove both interference and destroy entanglement. The situation would be far more palatable if the act of measuring was the skeleton key to destroy superposition. Complementarity says this is far more subtle. The mere possibility of that information leaking into the environment will do the trick. The universe conspires to disallow you to know.
Demystifier said:
To be sure, adherents of such interpretations often say that those restrictions refer to knowledge, without saying explicitly that those restrictions refer also to existence (ontology).
Actually, Quantum Bayesianists would explicity state that the restrictions do not apply to ontology. (I'm not an advocate myself) but they would say that any and all of these restrictions derive from the observer's knowledge.
Demystifier said:
Moreover, some of them say explicitly that things do exist even when we don't know it. But in my opinion, those who say so are often inconsistent with other things they say. In particular, they typically say that Nature is local despite the Bell theorem, which is inconsistent. It is inconsistent because the Bell theorem says that if something (ontology, reality, or whatever one calls it) exists, then this thing that exists obeys non-local laws. So one cannot avoid non-locality by saying that something is not known. Non-locality implied by the Bell theorem can only be avoided by assuming that something doesn't exist. Hence any version of Copenhagen/standard/orthodox interpretation that insists that Nature is local must insist that this interpretation puts a severe restriction on the existence of something, and not merely on the possibility to know something.
I am not sure you have characterized Bell's Theorem correctly here, but I wanted to say something else.
Modern physics separated itself from classical notions of ontology around the years of the EPR debates. We have, as a civilization a tools called QM and QFT, and those tools standing innocently on their own cannot identify what Einstein called objective "elements of reality". If the position of a particle is not an element-of-reality, then what is? Perhaps the objective element-of-reality we seek is the Quantum State (PBR Theorem). Or perhaps it is the Wave Function as some kind of extended wave ( as advocates of Many Worlds claim).
You will undoubtedly detect what you call "inconsistencies" in what people write about these topics. English has limits and it will fray at the edges. While the formal tools cannot identify elements of reality, the people who use them definitely think they can. These inconsistencies are unlikely to go away soon.
), remember the point is that there isn't a single sample space for the quantum observables, not that you can't get a sample space for the experimental outcomes (although even that single sample space will be "odd" with the observer embedded due to lack of a single sample space for the observables).